Estimating Frequency Moments of Data Streams Using Random Linear Combinations

The problem of estimating the kth frequency moment Fk for any nonnegative k, over a data stream by looking at the items exactly once as they arrive, was considered in a seminal paper by Alon, Matias and Szegedy [1, 2]. The space complexity of their algorithm is ˜O(n1− 1 k ). For k > 2, their technique does not apply to data streams with arbitrary insertions and deletions. In this paper, we present an algorithm for estimating Fk for k > 2, over general update streams whose space complexity is ˜O(n1− 1 k−1 ) and time complexity of processing each stream update is ˜O(1). Recently, an algorithm for estimating Fk over general update streams with similar space complexity has been published by Coppersmith and Kumar [7]. Our technique is, (a) basically different from the technique used by [7], (b) is simpler and symmetric, and, (c) is significantly more efficient in terms of the time required to process a stream update ( ˜O(1) compared with ˜O(n1− 1 k−1 )).

• Type: Conference
• Year: 2004
• Where: APPROX
• Authors: Sumit Ganguly
• Keywords: Algorithms, APPROX 2004, Data Streams, General Update Streams, Space Complexity